Operational envelopes for designing with soft actuators using a simplified continuum approach.

Liquid crystalline elastomers (LCEs) are soft materials capable of large, reversible deformations in response to external stimuli, making them promising alternatives to rigid actuators where compliance and untethered motion are crucial. However, adoption of LCEs in real-world systems has been hindered by the lack of practical modeling techniques that describe their functional behavior. Here, we present an analytical continuum framework based on decomposition of the actuation and elastic strains. Paired with existing hyperelastic models, this decomposition yields closed-form constitutive expressions which describe LCE behavior over a broad range of operating conditions. We experimentally validate the framework by showing it successfully predicts the stress state of an LCE across a variety of actuation sequences with low bias and error, indicating path independence for processes where elasticity dominates behavior. We further demonstrate the framework's flexibility by applying it to LCE fibers of different chemistry, and to a fiber having a complex hierarchical architecture; a capability crucial to employing LCE actuators in practical systems. Finally, we illustrate the utility of the resulting closed-form solutions through two design applications: quantitatively determining the coefficient of friction for a low-friction material, and a qualitative procedure for designing an LCE-actuated bistable mechanism. This work provides designers and researchers in soft robotics, microactuators, and compliant systems with a practical, rapidly deployable framework for characterizing and comparing thermoactive soft actuators.